IDEAS home Printed from https://ideas.repec.org/a/eee/ecosta/v36y2025icp55-72.html

Technical efficiency and inefficiency: Reliability of standard SFA models and a misspecification problem

Author

Listed:
  • Kumbhakar, Subal C.
  • Peresetsky, A.
  • Shchetynin, Y.
  • Zaytsev, A.

Abstract

It is formally proven that if inefficiency (u) is modelled through its variance, considered as a function of exogenous variables z, then the marginal effects of z on technical inefficiency (TI) and technical efficiency (TE) have opposite signs in the typical setup with a normally distributed random error and an exponentially or half-normally distributed u. This is true for both conditional and unconditional TI and TE. An example is provided to show that the signs of the marginal effects of z on TI and TE may coincide for some ranges of z. If the real data comes from a bimodal distribution of u, and a model is estimated with an exponential or half-normal distribution for u, the estimated efficiency and the marginal effect of z on TE could be wrong. Moreover, the rank correlations between the true and the estimated values of TE could be small and even negative for some subsamples of the data. This is a warning that in the case when the true (real life) distribution of the inefficiency is bimodal, commonly used standard SFA models could lead to wrong policy recommendations. The kernel density plot of the residuals is suggested as a diagnostic plot. The results are illustrated by simulations.

Suggested Citation

  • Kumbhakar, Subal C. & Peresetsky, A. & Shchetynin, Y. & Zaytsev, A., 2025. "Technical efficiency and inefficiency: Reliability of standard SFA models and a misspecification problem," Econometrics and Statistics, Elsevier, vol. 36(C), pages 55-72.
    • Handle: RePEc:eee:ecosta:v:36:y:2025:i:c:p:55-72
    DOI: 10.1016/j.ecosta.2021.12.006
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S2452306221001507
    Download Restriction: Full text for ScienceDirect subscribers only. Contains open access articles
    File URL: https://libkey.io/10.1016/j.ecosta.2021.12.006?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to

    for a different version of it.

    References listed on IDEAS

    as
    1. Lai, Hung-pin & Kumbhakar, Subal C., 2019. "Technical and allocative efficiency in a panel stochastic production frontier system model," European Journal of Operational Research, Elsevier, vol. 278(1), pages 255-265.
    2. Lee, Lung-Fei & Tyler, William G., 1978. "The stochastic frontier production function and average efficiency : An empirical analysis," Journal of Econometrics, Elsevier, vol. 7(3), pages 385-389, April.
    3. Ondrich, Jan & Ruggiero, John, 2001. "Efficiency measurement in the stochastic frontier model," European Journal of Operational Research, Elsevier, vol. 129(2), pages 434-442, March.
    4. Battese, George E. & Coelli, Tim J., 1988. "Prediction of firm-level technical efficiencies with a generalized frontier production function and panel data," Journal of Econometrics, Elsevier, vol. 38(3), pages 387-399, July.
    5. Jorge Galán & Helena Veiga & Michael Wiper, 2014. "Bayesian estimation of inefficiency heterogeneity in stochastic frontier models," Journal of Productivity Analysis, Springer, vol. 42(1), pages 85-101, August.
    6. Wu, Yanrui, 2000. "Measuring the performance of foreign direct investment: a case study of China," Economics Letters, Elsevier, vol. 66(2), pages 143-150, February.
    7. Mark Andor & Christopher Parmeter, 2017. "Pseudolikelihood estimation of the stochastic frontier model," Applied Economics, Taylor & Francis Journals, vol. 49(55), pages 5651-5661, November.
    8. Wang, Hung-Jen, 2003. "A Stochastic Frontier Analysis of Financing Constraints on Investment: The Case of Financial Liberalization in Taiwan," Journal of Business & Economic Statistics, American Statistical Association, vol. 21(3), pages 406-419, July.
    9. Kumbhakar, Subal C. & Sun, Kai, 2013. "Derivation of marginal effects of determinants of technical inefficiency," Economics Letters, Elsevier, vol. 120(2), pages 249-253.
    10. Jondrow, James & Knox Lovell, C. A. & Materov, Ivan S. & Schmidt, Peter, 1982. "On the estimation of technical inefficiency in the stochastic frontier production function model," Journal of Econometrics, Elsevier, vol. 19(2-3), pages 233-238, August.
    11. Sena, Vania, 2006. "The determinants of firms' performance: Can finance constraints improve technical efficiency?," European Journal of Operational Research, Elsevier, vol. 172(1), pages 311-325, July.
    12. Hung-Jen Wang, 2002. "Heteroscedasticity and Non-Monotonic Efficiency Effects of a Stochastic Frontier Model," Journal of Productivity Analysis, Springer, vol. 18(3), pages 241-253, November.
    13. Meryem Duygun & Levent Kutlu & Robin C. Sickles, 2016. "Measuring productivity and efficiency: a Kalman filter approach," Journal of Productivity Analysis, Springer, vol. 46(2), pages 155-167, December.
    14. Kumbhakar, Subal C. & Parmeter, Christopher F. & Tsionas, Efthymios G., 2013. "A zero inefficiency stochastic frontier model," Journal of Econometrics, Elsevier, vol. 172(1), pages 66-76.
    15. (Daniel) Kao, Ta-Wei & Su, Hung-Chung & Chen, Yi-Su, 2019. "The curvilinear relationships between structural embeddedness and productive efficiency: An exploratory study," International Journal of Production Economics, Elsevier, vol. 212(C), pages 176-185.
    16. Ruggiero, John, 1999. "Efficiency estimation and error decomposition in the stochastic frontier model: A Monte Carlo analysis," European Journal of Operational Research, Elsevier, vol. 115(3), pages 555-563, June.
    17. Meeusen, Wim & van den Broeck, Julien, 1977. "Efficiency Estimation from Cobb-Douglas Production Functions with Composed Error," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 18(2), pages 435-444, June.
    18. Aigner, Dennis & Lovell, C. A. Knox & Schmidt, Peter, 1977. "Formulation and estimation of stochastic frontier production function models," Journal of Econometrics, Elsevier, vol. 6(1), pages 21-37, July.
    19. Konstantinos Giannakas & Kien Tran & Vangelis Tzouvelekas, 2003. "Predicting technical effciency in stochastic production frontier models in the presence of misspecification: a Monte-Carlo analysis," Applied Economics, Taylor & Francis Journals, vol. 35(2), pages 153-161.
    20. Fang, Yiwei & Hasan, Iftekhar & Marton, Katherin & Waisman, Maya, 2014. "Bank valuation in new EU member countries," Economic Systems, Elsevier, vol. 38(1), pages 55-72.
    21. Andor, Mark A. & Parmeter, Christopher & Sommer, Stephan, 2019. "Combining uncertainty with uncertainty to get certainty? Efficiency analysis for regulation purposes," European Journal of Operational Research, Elsevier, vol. 274(1), pages 240-252.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Kumbhakar, Subal C. & Peresetsky, Anatoly & Shchetynin, Yevgenii & Zaytsev, Alexey, 2020. "Technical efficiency and inefficiency: Reassurance of standard SFA models and a misspecification problem," MPRA Paper 102797, University Library of Munich, Germany.
    2. Julia Schaefer & Marcel Clermont, 2018. "Stochastic non-smooth envelopment of data for multi-dimensional output," Journal of Productivity Analysis, Springer, vol. 50(3), pages 139-154, December.
    3. Zangin Zeebari & Kristofer Månsson & Pär Sjölander & Magnus Söderberg, 2023. "Regularized conditional estimators of unit inefficiency in stochastic frontier analysis, with application to electricity distribution market," Journal of Productivity Analysis, Springer, vol. 59(1), pages 79-97, February.
    4. Andor, Mark A. & Parmeter, Christopher & Sommer, Stephan, 2019. "Combining uncertainty with uncertainty to get certainty? Efficiency analysis for regulation purposes," European Journal of Operational Research, Elsevier, vol. 274(1), pages 240-252.
    5. Mark Andor & Frederik Hesse, 2014. "The StoNED age: the departure into a new era of efficiency analysis? A monte carlo comparison of StoNED and the “oldies” (SFA and DEA)," Journal of Productivity Analysis, Springer, vol. 41(1), pages 85-109, February.
    6. Mark A. Andor & David H. Bernstein & Stephan Sommer, 2021. "Determining the efficiency of residential electricity consumption," Empirical Economics, Springer, vol. 60(6), pages 2897-2923, June.
    7. Ahn, Heinz & Clermont, Marcel & Langner, Julia, 2023. "Comparative performance analysis of frontier-based efficiency measurement methods – A Monte Carlo simulation," European Journal of Operational Research, Elsevier, vol. 307(1), pages 294-312.
    8. Getu Hailu & B. James Deaton, 2016. "Agglomeration Effects in Ontario’s Dairy Farming," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 98(4), pages 1055-1073.
    9. Alexander D. Stead & Phill Wheat & William H. Greene, 2023. "On hypothesis testing in latent class and finite mixture stochastic frontier models, with application to a contaminated normal-half normal model," Journal of Productivity Analysis, Springer, vol. 60(1), pages 37-48, August.
    10. Mai, Nhat Chi, 2015. "Efficiency of the banking system in Vietnam under financial liberalization," OSF Preprints qsf6d, Center for Open Science.
    11. Hou, Zhezhi & Kumbhakar, Subal C. & Zhao, Shunan, 2024. "Productivity and efficiency: Do we need a bridge?," International Journal of Production Economics, Elsevier, vol. 274(C).
    12. Christopher F. Parmeter & Hung-Jen Wang & Subal C. Kumbhakar, 2017. "Nonparametric estimation of the determinants of inefficiency," Journal of Productivity Analysis, Springer, vol. 47(3), pages 205-221, June.
    13. Mark Andor & Frederik Hesse, "undated". "The StoNED age: The Departure Into a New Era of Efficiency Analysis? An MC study Comparing StoNED and the "Oldies" (SFA and DEA)," Working Papers 201285, Institute of Spatial and Housing Economics, Munster Universitary.
    14. Phill Wheat & Alexander D. Stead & William H. Greene, 2019. "Robust stochastic frontier analysis: a Student’s t-half normal model with application to highway maintenance costs in England," Journal of Productivity Analysis, Springer, vol. 51(1), pages 21-38, February.
    15. Centorrino, Samuele & Pérez-Urdiales, María, 2023. "Maximum likelihood estimation of stochastic frontier models with endogeneity," Journal of Econometrics, Elsevier, vol. 234(1), pages 82-105.
    16. Orea, Luis, 2019. "The Econometric Measurement of Firms’ Efficiency," Efficiency Series Papers 2019/02, University of Oviedo, Department of Economics, Oviedo Efficiency Group (OEG).
    17. Young Hoon Lee, 2009. "Frontier Models and their Application to the Sports Industry," Working Papers 0903, Nam Duck-Woo Economic Research Institute, Sogang University (Former Research Institute for Market Economy), revised 2009.
    18. Sakouvogui Kekoura & Shaik Saleem & Doetkott Curt & Magel Rhonda, 2021. "Sensitivity analysis of stochastic frontier analysis models," Monte Carlo Methods and Applications, De Gruyter, vol. 27(1), pages 71-90, March.
    19. Subal C. Kumbhakar & Christopher F. Parmeter & Valentin Zelenyuk, 2022. "Stochastic Frontier Analysis: Foundations and Advances I," Springer Books, in: Subhash C. Ray & Robert G. Chambers & Subal C. Kumbhakar (ed.), Handbook of Production Economics, chapter 8, pages 331-370, Springer.
    20. Samuele Centorrino & María Pérez‐Urdiales & Boris Bravo‐Ureta & Alan Wall, 2024. "Binary endogenous treatment in stochastic frontier models with an application to soil conservation in El Salvador," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 39(3), pages 365-382, April.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:ecosta:v:36:y:2025:i:c:p:55-72. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/econometrics-and-statistics .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.